Numerical study on particle velocity and sound pressure by circular flat transducers

Abstract

During years of investigation on the ultrasonic near field, only the sound pressure, namely, the spatial distribution of velocity potential, has been studied. In this report, particle velocity and acoustic impedance density of the ultrasonic field by circular flat transducers are derived and computed together with sound pressure. Sound pressure is proportional to the velocity potential of the ultrasonic field. Its particle velocity is the space differential of the velocity potential, and the acoustic impedance density is the quotient of the sound pressure by the particle velocity. On the axis of the transmitting circular flat transducer, the phase delay of the sound pressure has peculiar leaps. But, acoustic impedance density has constant leaps from −π/2 to π/2, where the amplitude is zero. The mean value over a receiving coaxial circular flat transducer is also computed changing the ratio of the radius (a) of the circular flat transducer to the wavelength (λ) of the ultrasonic wave. Mean amplitudes of sound pressure, particle velocity, and acoustic impedance density are tabulated with the normalized distance (zλ/a2) in the computing precision of 0.1%. The mean amplitude of the z component of the particle velocity is always less than 1.0 and seems to be an appropriate response for the ultrasonic system of a pair of circular flat transducers.